Finite Group Databasebeta

← #14655644

Subgroups — #14655644

Order 2816.

498 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079744C211yesmaximal, characteristic
2#13079012C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic, complemented
4#13067297C211yesmaximal, characteristic, complemented
5#13067068C211yesmaximal, characteristic
6#13066453C211yesmaximal, characteristic, complemented
7C2×C11×#500C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#500—22no—
12C11×#500—22no—
13C2×C11×#107—22no—
14C2×C4×C8×C11C2211yescharacteristic
15#10622706—21no—
16#10622702—22no—
17#10622701—21no—
18#10622701—21no—
19#10622697—22no—
20#10622692—21no—
21#10622581—22no—
22#10622579—22no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622184—22no—
27#10622168—22no—
28#10622097—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C2×#4339—21no—
32C22×C8×C11—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D412yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D412yes—
45C2×C42×C11C2311yescharacteristic
46#66983—21no—
47#66983—21no—
48C2×#4318—21no—
49C2×#4318D412yes—
50#66928—21no—
51#66927D411yescharacteristic
52C4×D44—21no—
53C4×D44—21no—
54#66922D411yescharacteristic
55C11×#107—28no—
56C4×C8×C11—21no—
57C4×C8×C11D412yes—
58C22⋊(C11⋊C8)—21no—
59#66874—24no—
60#66873—24no—
61#66873—24no—
62#66872—24no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69#10164—111nomaximal, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—82no—
75C2×Q8×C11—82no—
76C22×C4×C11—22no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×C22⋊D11—41no—
82#4339—42no—
83#4339—42no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×Dic22—21no—
89C2×C8×C11—24no—
90C2×C8×C11—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107#4318—22no—
108#4318—22no—
109#4318—42no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—41no—
113#3227—111no—
114C2×#500D1111yescharacteristic, complemented
115#3141—111no—
116#1997—111no—
117#1548—111no—
118#1492—111no—
119#1278—111no—
120C23×C11#12111yescharacteristic
121C22×D11—41no—
122Q8×C11—82no—
123Q8×C11—82no—
124Q8×C11—82no—
125Q8×C11—82no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—82no—
131C2×C4×C11—82no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12711yescharacteristic
138C2×C4×C11#13512yes—
139C2×C4×C11#13712yes—
140C22⋊D11—82no—
141C2×Dic11—41no—
142D44—42no—
143D44—42no—
144D44—42no—
145C4×D11—81no—
146C4×D11—81no—
147Dic22—42no—
148C8×C11—24no—
149C11⋊C8—42no—
150C11⋊C8—42no—
151C11⋊C8—81no—
152#532—111no—
153C2×C4⋊Q8C2×D1111yescharacteristic
154C2×C4⋊Q8C2×D1111yescharacteristic
155#500—22no—
156#500—22no—
157#498—221no—
158#489—222no—
159#487—221no—
160#486—221no—
161#486—221no—
162#481—222no—
163#476—222no—
164#431—111no—
165C2×#107—22no—
166#423—111no—
167#417—222no—
168C4×M16—111no—
169C2×C4×C8C2×D1111yescharacteristic
170#343—222no—
171#333—222no—
172D4⋊C8—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11#39211yescharacteristic
176C22×C11#46412yes—
177C2×D11—81no—
178C2×D11—81no—
179C2×D11—81no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—82no—
183C4×C11—82no—
184C4×C11#45212yes—
185C4×C11#45612yes—
186C4×C11#47212yes—
187C4×C11#49511yescharacteristic
188C4×C11#49711yescharacteristic
189Dic11—81no—
190C2×#41—221no—
191C22×Q8—21no—
192C22×Q8—21no—
193C2×M16—112no—
194C2×M16—221no—
195C22×C8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—111no—
204C4⋊Q8C22⋊D1112yes—
205#127—111no—
206#124—221no—
207#121—221no—
208#121—221no—
209C4×D4—221no—
210C4×D4—221no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C22⋊D1112yes—
215C2×C42C22×D1111yescharacteristic
216#107—28no—
217#106—224no—
218C4⋊C8—112no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221#103—224no—
222#102—224no—
223#102—224no—
224C22⋊C8—221no—
225#97—221no—
226C4×C8—21no—
227C4×C8—221no—
228C4×C8—221no—
229C4×C8C22⋊D1112yes—
230C2×C11—22no—
231C2×C11#200511yescharacteristic
232C2×C11#201511yescharacteristic
233C2×C11#201811yescharacteristic
234D11—161no—
235#41—442no—
236#41—442no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—82no—
242C2×Q8—82no—
243C2×Q8—221no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4—221no—
247C2×D4—441no—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4—441no—
251C22×C4D4×D1111yescharacteristic
252C22×C4#434111yescharacteristic
253C22×C4C2×C22⋊D1111yescharacteristic
254M16—222no—
255M16—222no—
256M16—442no—
257C2×C8—24no—
258C2×C8—22no—
259C2×C8—222no—
260C2×C8—222no—
261C2×C8—441no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C22⋊C4—441no—
273C22⋊C4—441no—
274C42D4×D1111yescharacteristic
275C42D4×D1111yescharacteristic
276C42C2×C22⋊D1111yescharacteristic
277C42C2×C22⋊D1111yescharacteristic
278C11#1016411yescharacteristic, complemented, Sylow
279C23—441no—
280C23#6699211yescharacteristic
281Q8—82no—
282Q8—82no—
283Q8—82no—
284Q8—82no—
285Q8—442no—
286D4—442no—
287D4—442no—
288D4—442no—
289D4—882no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—82no—
295C2×C4—82no—
296C2×C4—441no—
297C2×C4—881no—
298C2×C4—881no—
299C2×C4#6697112yes—
300C2×C4#6697212yes—
301C2×C4#6699011yescharacteristic
302C2×C4#6699011yescharacteristic
303C2×C4#6699111yescharacteristic
304C2×C4#6699211yescharacteristic
305C2×C4#6699311yescharacteristic
306C2×C4#6700611yescharacteristic
307C8—24no—
308C8—442no—
309C8—442no—
310C8—881no—
311C22—21no—
312C22—21no—
313C22—881no—
314C22—881no—
315C22—881no—
316C22#1062279812yes—
317C22#1062283611yescharacteristic
318C4—21no—
319C4—21no—
320C4—82no—
321C4—82no—
322C4—881no—
323C4#1062270812yes—
324C4#1062277312yes—
325C4#1062280012yes—
326C4#1062280311yescharacteristic
327C4#1062280411yescharacteristic
328C2—22no—
329C2—1761no—
330C2#1306965211yescharacteristic
331C2#1306970711yescharacteristic
332C2#1306972311yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#500C2
socleC22×C11#392
prime radical#10623008C22
hypercenterC2×#500D11
hypocenterC11#10164
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#500

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13069606C2semidirect
4. #13067297C2semidirect
6. #13066453C2semidirect
7. C2×C11×#500C2semidirect
114. C2×#500D11semidirect
278. C11#10164semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130797442
#130790122
#130696062
#130672972
#130670682
#130664532
C2×C11×#5002
#1016411